Hi Jeff,
To get into your Weller base, carefully pry out the 4 rubber feet with an old sturdy knife blade, exposing 4 Phillips screws underneath.

I have been looking for a wiring schematic for my similar defective Welller EC2001 Soldering Station, but so far, I only found the parts list and parts drawing.
See <www.arcade-electronics.com/cooper /wellerparts.htm>

My EC2001 has normal LED display on the front, but the iron doesn't heat. The internal 5V DC regulator circuit in the base is ok, and there is 24 V on some of the 5 pins. I hope someone will pass along the voltage and resistance readings on their Base Unit & iron, so I can figure out if I need the EC234 Heater, &/or the temperature controller. My Base uses the EC 1201A or EC1201P irons.